Model Output Statistics (MOS) Numerical Weather Prediction (NWP) models calculate the future state of the atmosphere at certain points of time (forecasts). The calculation of these forecasts is based on observation data and the solving of atmospheric equations. The forecasts are produced for so-called grid points which, in the model, are distributed over the entire globe in a grid-like pattern. NWP models do have weaknesses. They simplify the conditions at the Earth s surface as they see it as a network of grid points. Small-scale effects cannot be calculated to any desired degree of accuracy. It is also not possible to explicitly represent particular desired variables or geographical points. Furthermore, the forecasts of NWP models also have systematic errors. Model Output Statistics (MOS) procedures are used to optimise the direct forecast outputs of NWP models by means of statistical relationships determined beforehand between the Direct Model Output (DMO) and meteorological observation data. The aim is to reduce any deviation that might exist between the model forecast and observation data to the smallest possible degree. For this purpose, predictor parameters that can significantly contribute to explain the variability in the parameters of interest (predictants) are selected and interlinked using the multiple linear regression technique based on the long-term set of historic observation and model data. Model Output Statistics (MOS) is a statistical post-processing technique that determines the systematic dependencies between the predictands and the given predictors (DMOs and current observation data) and applies them to a specific meteorological situation. Why MOS? In practice, due to their high accuracy, MOS procedures have proven to be valuable interpretation tools for the meteorologists at the DWD. Among them, particularly MOSMIX is regularly consulted in routine operations. The MOS procedures used at the DWD are updated on a regular basis by including the latest measurement and model forecast series and by adding new stations.
Model Output Statistics MIX (MOSMIX) The DWD s fully automatic MOSMIX procedure optimises and interprets the calculations of the DWD s and ECMWF s numerical models ICON and IFS, respectively; it combines these with one another and computes statistically optimised weather forecasts in the form of point forecasts. This provides updated, statistically corrected forecasts for the next 10 days for more than 5,000 locations worldwide. Most of the forecast locations are situated in Germany and Europe (see fig. 1). Fig. 1: MOSMIX forecasts visualized for Europe; here: present significant weather calculated on 02.08.2017, 3:00 UTC, for 03.08.2017, 15:00 UTC. MOSMIX forecasts (point forecasts) include nearly all weather parameters usually measured at observation stations: - temperature and dew point at 2 m - wind speed - wind direction - maximum wind gusts at 10 m - expected rainfall total - type of precipitation (rain or snow) - air pressure - sunshine duration and many more. It also provides forecasts for weather elements, such as visibility, for example, for which the numerical models initially do not provide any values; these forecasts are obtained through statistical parametrisations and interpretation in MOSMIX. MOSMIX forecasts also include probabilistic
forecasts, i.e. probability statements regarding the occurrence of strong wind gusts or high precipitation events, for example. Basic features of MOSMIX MOSMIX forecasts (point forecasts) are calculated in two steps: The first step is to postprocess the outputs from the two numerical models ICON (DWD) and IFS (ECMWF) statistically. The results of this are the ICON-MOS and IFS-MOS forecasts. The second step is to combine the latter in a statistically optimal manner. Due to the fact that MOSMIX forecasts are updated hourly, they always take account of the latest observation data. This guarantees a very high forecast quality during the first couple of forecast hours. The results of MOSMIX also provide a basis for the DWD s official weather forecasts and weather warnings. Boundary conditions and procedures for statistical optimisation The statistical optimisation and interpretation of ICON and IFS model outputs are based on long times series of meteorological observations at weather stations and numerical model calculations for the same sites. To obtain up-to-date, statistically optimised forecasts the systematic differences and statistical interrelations of the time series from the past are analysed and current forecasts are adapted accordingly. Example: If it is found that past numerical model temperature values in rain conditions were often higher than the values actually observed, new ongoing model calculations of the temperature during rain will lower the computed values using so-called MOS coefficients in order to obtain improved forecasts. Analysis and parameterisation of such statistical interrelations are done mathematically using stepwise multiple linear regression (MLR). This also allows the statistical interpretation and forecasting of weather elements which were initially not calculated by the numerical models. Probability statements are equally produced by searching the time series for statistical interrelations between the model calculations and the observed frequency of occurrence of the weather events in question. The time series of observation and model data used for MOS procedures should go back as many years as possible in order to obtain reliable analyses of such statistical interrelations, particularly for extremely heavy and rare weather events. The series of forecast data used in the ECMWF s IFS are currently reaching back 15 years, the DWD s ICON model is based on forecast data series starting from 2015. At present, the DWD still uses earlier numerical forecasts in order to have a longer data series of forecast data available. Breaks in the time series due to model changeovers or changes within the numerical models are taken into account statistically.
MOSMIX cycle Fig. 2: MOSMIX cycle. Long-term series of numerical model forecasts (ICON and IFS) and station data are analysed using MLR techniques. The calculated statistical corrections and parameterisations are used in routine operations to compute optimised weather forecasts on the basis of the current model forecasts (MOSMIX point forecasts). Once optimised by means of the MOS coefficients, the forecasts of both models ICON (DWD) and IFS (ECMWF) are put together to obtain the best possible combined forecast. Like in the Development part, this is done by combining long-term time series of the forecasts that have already been optimised, complementing these by observation data and then analysing them using MLR. This finally leads to uniform weather forecasts that take account of both the different information contents and the specific advantages of the two numerical models and provide the best possible forecast skill overall. As the systematic dependencies, in particular those concerning ground-level weather parameters such as 2m temperature, highly depend on the weather station in question, the statistical corrections are individual for each station. The corrections also depend on the start time of the forecast and on the time for which the forecast is valid. Account is also taken of daily and annual systematic variations. This is true for both the optimisation of the numerical models and the combining of optimised forecasts. MOSMIX uses over a billion statistical corrections and parameterisations which are calculated individually on the basis of time series reaching back up to 15 years and are due to the facts that - a number of around 5,400 national and international stations are taken into account; - there are 24 forecast runs per day; - the forecast periods cover up to +240h; - the statistical processing takes account of all four seasons;
Availability of data MOSMIX forecasts are computed for around 5,400 stations around the world. The number of stations may change at irregular intervals due to continuous quality assurance. Around 2,800 of the stations worldwide are so-called development stations (or main stations ), i.e. MOS coefficients are calculated explicitly for every single station based on historical observations and model data and for a station-specific number of parameters (depending on the availability of the observation data). The other 2,600 forecast points are so-called interpolation stations. The forecasts for these stations are calculated by interpolation (horizontal, vertical, temporal) based on neighbouring stations for which explicit forecast values are available. Production Cycle as of 15 March 2018 On 15 March 2018 a new MOSMIX version with a forecasting time step of one hour and a maximum forecasting time of +240h has been introduced. MOSMIX forecasts are available 24x daily, about 25 minutes after every full hour. The first 24 forecast hours feature hourly updates and include the latest observational data. In contrast, the forecasting hours +25 to 240 are updated only four times daily at 04, 10, 16 and 22 UTC. Data Format and Availability as of 15 March 2018 In the course of the introduction of the new MOSMIX version, the data format of the MOSMIX forecasts has been switched to a standardized KML format, for which a special DWD namespace has been published (see right column). Details about the KML namespace and the meaning of the individual meteorological elements can be found in the directory https://opendata.dwd.de/weather/lib/, whereupon the following single files are of relevance: pointforecast_dwd_extension_v1_0.xsd DWD-specific KML namespace, which explains the setup of the MOSMIX data files MetElementDefinition.xsd Scheme of the element list (structural setup) MetElementDefinition.xml Description of the individual meteorological elements used in the KML files. In order to balance various user requirements of extended forecast parameters and performance issues, two separate data sets are provided: MOSMIX_S (24x daily, 40 parameters, up to +240h): from 15 March 2018 MOSMIX_L (4x daily, 115 parameters, up to +240h): from 15 April 2018 Please note that the pre-operational test data are not quality assured. Incorrect individual forecast values and missing data may occur.